Suppose we doubt that the probability of male birth is exactly 50%, but are willing to assume that the gender of successive offspring are independent.

What is the best estimate of the probability of a male birth based on the observed data?
What is the probability of 0, 1, 2, 3, 4, and 5 male births out of 5 births based on the estimate obtained.
How do we test the hypothesis that the gender of successive offspring are independent based on the model above.

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